# Vacuum Energy - Pair Production Confusion

1. Jul 5, 2009

### benk99nenm312

So, let's get this straight . Black hole evaporation is, by the layman's version, supposedly due to a negative mass particle entering the black hole, while it's counterpart leaves, as radiation. These particles are formed near the black hole by vacuum fluctuations (i.e. pair production). I'm not entirely certain, but when a pair is formed in vacuum fluctuations, I've always assumed they both had positive mass (since antimatter and matter both have positive mass when real). So I have a contradiction here. Is it something to do with the fact that they are virtual particles? But even so, what allows a virtual particle to have negative mass? What's going on here?

2. Jul 5, 2009

### humanino

Virtual particles can have pretty much any mass, positive, negative, imaginary if you want. The above description of BH evaporation entails the concept of local vs global energy in general relativity, which is yet another complication to the problem. Take it that way : the zero of energy is not the same on the horizon and at infinity. Among the two particles of the pair created, although both of them locally carry positive energy, one of them will have less energy than the other, and at infinity it looks like they carry nothing on average. So at infinity, it looks like the one carrying less energy, which is more likely to fall, actually carried negative energy.

Sorry, I know this is quite sketchy, but it's a long topic.

3. Jul 5, 2009

### benk99nenm312

I'm not sure I follow you here. Why would one particle have less energy than the other?

- yeah, this is a sketchy topic

4. Jul 5, 2009

### benk99nenm312

Also, I think a problem is: what exactly do the virtual particles created by the vacuum fluctuations anhilate into? By that I mean, what comes out.. a virtual photon.. nothing..?

5. Jul 5, 2009

### humanino

Usually we are given a background and a field on top of it. Then you Fourier transform your field and the proper modes with negative frequency are re-interpreted as anti-particle with positive energy. So the sketchy argument is that what is locally zero near the horizon allowing one to define antiparticle there does not trivially transport to infinity, because of a non-negligible contribution from the gravitational field itself. From infinity it looks like two particles (not able to tell antiparticles from particles) with positive energy, but one has less energy and is therefore more likely to fall. Eventually what comes out of the BH seems like a thermal radiation of both particles and antiparticles, measured at infinity.

I wish someone more competent could help.

6. Jul 5, 2009

### benk99nenm312

You're doing fine , but i agree... where is everyone?

7. Jul 6, 2009

### Chronos

Virtual particles are an artifact of the uncertainty priciple. They dont last long enough to be of any real consequence. In most quantum gravity theories they are, however, of great importance.

8. Jul 6, 2009

### humanino

This is a rather strange statement honestly speaking. Turn off first order corrections and pretty much all measurements in the realm of high energy physics are changed, I'm referring now to so-called radiative corrections. Historically, we obtained evidence for the correctness of renormalization thanks to them for instance. It is beyond my understanding that anyone would consider them "an artifact" without "any real consequence".

9. Jul 6, 2009

### benk99nenm312

Many physicists deny the existence of their own mathematical conclusions. However, without them, we wouldn't have an accurate explanation for electromagnetism. But, I don't want to talk about that. I was wondering if anyone had an answer to my question in post number 3, or 4 as seen numerically on the page.

10. Jul 6, 2009

### Sourabh N

I think it has something to do with Einstein's that equation E = mc^2. Energy in some(?) form is converted to mass when that pair is produced. Someone please support that! or correct me :uhh:

Last edited: Jul 6, 2009
11. Jul 8, 2009

### malawi_glenn

no they are a mathematical artifact by perturbation formulation of a calculation in QFT.

12. Jul 8, 2009

### Chronos

Another failed attempt at humor. Pair production is only relevent under unusual circumstances - like near the event horizon of a black hole. It also manifests itself as the casimir effect. It is undoubtedly real and well confirmed by experimental evidence. Virtualy particles ordinarily self annihilate, crashing one into the other. Near an event horizon, the 'positive' energy particle can escape, leaving the other particle holding the bag, so to speak. The event horizon thus effectively 'bleeds' energy over time [Hawking radiation]. An even weirder effect occurs in the case of Unruh radiation, but is equally well founded based on the same premises.

13. Jul 8, 2009

### malawi_glenn

But then one can say that ee scattering is also proving the existence of virtual particles, of course Casimir Effect etc CAN BE EXPRESSED in terms of virtual particles, they can be formulated with different concepts, e.g. the Casimir effect can be formulated just using a zero-point energy. etc. Virtual particles are just a tool.

14. Jul 8, 2009

### benk99nenm312

So, are you saying that nothing comes out of the annihilation?

I know virtual particles are a tool, but I'm trying to understand whether empty space, consisting of a few virtual particle pairs, produces any energy.

15. Jul 8, 2009

### malawi_glenn

produces as in increasing the total energy? No

16. Jul 8, 2009

### benk99nenm312

Interesting. So it's like a negative and positive mass virtual particle pair will completely annhilate, with nothing left over. Is that correct?

17. Jul 8, 2009

### malawi_glenn

Energy is mass so net energy is the same all the time

18. Jul 8, 2009

### benk99nenm312

Well, I think I understand where you're coming from... this is a confusing subject for me. So, let's just say this. I have one virtual particle pair created in the vacuum. They annhilate. Would there be something that comes out of the annhilation, to balance the total energy of the virtual pair, or would they completely annhilate, leaving nothing to come out? (When I say come out, I mean like a photon, or a virtual photon).

Sorry, my knowledge on this subject is not great.

19. Jul 8, 2009

### malawi_glenn

they would produce energy, the amount of energy they got when they became "created" by the vacuum.

E = {pair created}: E_0 + E_virtual-pair ={pair annihilated}: E

20. Jul 8, 2009

### benk99nenm312

Oh, I see. So, in what form is that energy?

Is this dark energy?